Micro Programmable Object Navigation
Gadget (µ-PONG)
for Studying Electroosmotic
Flow in a PDMS Microchannel
Brittany Rohrman
Background and Significance:
One of the most useful features of microfluidic devices, in the context of biological
research, is their ability to serve as tiny fluidic enclosures for either individual or small
collections of cells. The small volume of such enclosures can enable the in vitro study of cellcell interactions as well as paracrine and autocrine signaling events that would be difficult to
achieve in traditional large Petri dish cell culture environments, which typically have extremely
large (and non-physiological) ratios of cell media fluid volume to cell volume. Microfluidic
devices are more comparable to in vivo tissue environments because they are fabricated to
house cells in small fluidic volumes. However, one constraint on the long-term observation of
cells enclosed in tiny fluidic enclosures is the need to replenish the nutrient solutions
surrounding the cells. Another constraint when utilizing microfluidic devices is the need for very
low flow rates capable of manipulating cells without disrupting pre-established biochemical
diffusion gradients. These low-flow techniques typically require expensive (~$3000) precision
syringe pumps to provide on-demand, extremely low fluid flow rates. An attractive alternative to
this expensive mechanical syringe pump technology is an electro-kinetic technique that can
induce low volume electroosmotic flow in microchannels.
Objective:
The goal of my senior honors thesis project is to create an automated testing system (µPONG) for characterizing electroosmotic flow (EOF) in poly(dimethylsiloxane) (PDMS) devices.
My hope is that this system will be used to characterize EOF in particular PDMS devices
intended for biological research in order to demonstrate the possibility of utilizing EOF as a
pumping system in such devices. The basic premise of my research is that by using the
computer-controlled µ-PONG system to control the movement of a polystyrene bead in a PDMS
microchannel, the recorded motion of the bead will serve as a measure of the electroosmotic
flow strength over time. Hence, this characterization may be an important factor in the design of
biological experiments. Once the system is optimized for well-controlled fluid delivery, the µPONG system may also serve as a tool for manipulating particles or cells in PDMS microfluidic
devices.
Introduction:
Poly(dimethylsiloxane), or PDMS, is a polymer often used to construct microscopic or
nano-scale channels. Because PDMS is permeable to gases, nontoxic to cells, and optically
clear,1 these channels often serve as an optimal environment in which electroosmotic flow
(EOF) is used to manipulate cells2 and biomolecules3 for study. In experiments utilizing EOF, a
potential difference is applied across an oxidized PDMS channel filled with a buffer. Cations
from the buffer are attracted to anions bound to the walls of the channel, forming what is known
as the electric double layer (EDL), which is only a few nanometers wide (Figure 1).
2
Oxidized PDMS
EDL
Electroosmotic Flow
Figure 1: Electroosmotic flow (EOF). When an electric field
is applied across the channel, positive ions from electric
double layer (EDL) move toward the negative electrode,
dragging the rest of the solution in that direction.
The potential difference causes the layer of cations to move toward the negative electrode,
pulling the rest of the solution in the same direction via viscous drag.4 This phenomenon is
known as electroosmotic flow. The flow is often quantified by the electroosmotic mobility,
eo 

,

which is defined by  (the permittivity of the solution),  (the zeta potential), and  (the
viscosity of the solution).5 Another common measure of electroosmotic flow is the
electroosmotic velocity, veo, which is closely related to the electroosmotic mobility. The
electroosmotic velocity is defined as
veo  E eo ,
where E denotes the applied electric field.6
Electroosmotic flow has been implemented in a wide variety of applications, often
serving as a pump in lab-on-a-chip (LOC) microfluidic devices.7 LOC devices allow bioassays
to be performed on a much smaller scale, reducing the time and volume of reagents required for
traditional methods. Electroosmotic flow is ideal for use in LOC devices because it requires no
moving parts and may be controlled very precisely, unlike pressure-driven flow. Another
potential advantage of EOF is that the velocity of the fluid is the same throughout the cross
section of the channel (plug flow), while the velocity profile of pressure-driven fluid flow is
parabolic (Poiseuille flow). However, the strength of the EOF in oxidized PDMS channels has
been reported to attenuate over a period of just a few hours.8 This research aims to quantify
this effect by studying the movement of fluorescent polystyrene beads manipulated by EOF in a
PDMS microchannel. Once these time-dependent characteristics of electroosmotic flow are
known, use of the flow may be optimized for various microfluidic applications.
3
Methods:
Microfabrication of PDMS devices
PDMS microchannels were made using standard microfabrication and soft lithography
methods (Figure 2). First, SU-8 photoresist on a silicon support is exposed to ultraviolet light
through a mask. The light cures the exposed photoresist, leaving the photoresist obscured by
the mask uncured. The uncured photoresist is then dissolved, leaving a raised pattern defined
by the mask called a master. After further surface treatments, uncured (liquid) PDMS is poured
onto the master and degassed to remove bubbles. The PDMS is then baked overnight to
solidify the polymer. After exposure to an oxygen plasma for 30 seconds to create negative
charges (Si-0–) on the PDMS surface (for our devices, a PDC-32G Plasma Cleaner/Sterilizer
was used on the “high” power setting), the PDMS is irreversibly bonded to a clean glass slide.
Our devices were filled with 10 mM monobasic potassium phosphate buffer at pH 7.0
immediately after plasma bonding. Carboxylated or uncarboxylated fluorescent polystyrene
beads (Polysciences, Inc. Fluoresbrite YG microspheres, CV = 5%) with diameters of 3 or 10
microns were used. Several microliters of beads at concentrations between 0.01 and 0.001%
solid were deposited into one end of the channel using a micropipette. In some experiments,
the pressure was equalized by pumping additional buffer into the channel. Then a computer
program was used to control and/or record the movement of the bead.
UV light
mask
1
photoresist
and silicon wafer
2
master
3
PDMS poured
into master
4
PDMS bonded
to glass
Figure 2: Soft lithography and microfabrication of PDMS channels.
The µ-PONG system
The µ-PONG system consists of a DAQ board, an external voltage switching circuit, and
a camera, which are controlled by a computer program written in a LabView programming
environment (Figure 3). The computer is connected to a National Instruments USB-6009 device
capable of producing an analog voltage ranging from zero to five volts or a digital control signal
(on = 0 volts, off = 5 volts) (Figure 4). To increase the range of possible voltages used for
experiments, an external circuit was designed and built to amplify the USB analog voltage by a
factor of 1.83 (Figure 5). A digital voltage channel from the USB device is also connected to the
4
circuit in order to control the directional sense (or sign) of the voltage at the output leads, such
that changing the state of the digital signal reverses the direction of the potential difference
across the leads. The analog output signals from this external circuit establish a voltage
between the electrodes that are inserted at each end of the microfluidic channel (Figure 6).
Thus, a voltage is set up across the channel that causes electroosmotic flow.
Gold electrode
Goal posts
PDMS
Glass
Polystyrene bead
-fluidic
device
Control box
Objective
-scope
stage
Dichroic
mirror
Excitation
Ex filter
Em filter
Camera /
detector
Computer
Figure 3: Schematic diagram of the µ-PONG system. Two electrodes from
the control box are inserted at each end of the PDMS microchannel, which
is imaged through a camera via fluorescence microscopy. A LabView
program displays the image from the camera and communicates with a
USB device and external circuit housed inside a control box. When the
bead reaches a virtual goalpost, the program detects the bead and reverses
the direction of the voltage across the channel, keeping the bead moving
between the goalposts.
The LabView program continually retrieves and displays an image of the microchannel in
real time. Based on the image, the user utilizes the software to specify two virtual “goalpost”
regions of interest located at opposite ends of the imaged channel, typically about 200 microns
apart. The pixel intensities of the goalposts are compared to a user-specified target intensity
value in order to determine if a bright bead has entered a goalpost region. When that target
intensity value is reached or exceeded, the program sends a signal via the USB port to the DAQ
device, changing the state of the digital voltage channel connected to the external circuit. That
signal reverses the polarity of the voltage across the PDMS microchannel, thereby reversing the
direction of the EOF (see Appendix A for block diagram of LabView program). This strategy
works well because fluorescence microscopy is used to capture the image of the channel,
causing the bead to appear brighter than anything else in the channel. Thus, whenever the
bead reaches a region of interest, the reversal of the EOF causes it to move toward the other
region of interest, where the process is repeated. The bead moves back and forth between the
regions of interest much like a ball moves back and forth during a game of ping pong, allowing
experiments to run for long periods of time.
5
Figure 4: The NI-USB
6009
device
relays
signals
from
the
computer to the circuit.
Figure 5: The external
circuit
amplifies
the
signal from the USB
device and changes the
direction of the voltage.
Figure 6: The electrodes
at each end of the PDMS
channel
cause
EOF,
which moves the bead.
The LabView user interface
Before the program is run, the user can specify channel width, device age, and
other comments in a table on the front panel labeled “parameters” (Figure 7). On the
front panel, the user may also specify the physical digital and analog output channels of
the USB device as well as their minimum and maximum voltages, although these are
already set to default values. The user clicks the “run” arrow to execute the program.
Instructions for saving the parameters and subsequent data are displayed before the
user is asked to specify a *.lvm filename and location to save the parameter table. On
the front panel, the user specifies the desired analog output voltage to send to the USB
device via a slider. The user must also specify the pixel locations of the regions of
interest. The “left indicator” and “right indicator” are illuminated each time the bead is
detected in the specified region of interest during the experiment.
Figure 7: LabView interface. The user may specify the location of
the virtual goalposts, the detection threshold, and the voltage
6
across the channel. The user may also pause the EOF, save data,
record a video, and specify the mode of the system (“manual” or
“automatic”).
The user may run the program in a manual or automatic mode by clicking the
“Manual/Auto” button on the front panel. The “manual” mode allows the user to switch
the polarity, and thus the direction of the EOF, by clicking the “Left/Right” button on the
front panel. The “auto” mode detects the bead at the regions of interest and reverses
the polarity automatically. The user may also turn on or off the voltage across the
channel by clicking the “Pause/Run” button on the front channel. The “pause” mode
simply sets the voltage to zero, while the “run” mode establishes the voltage set on the
slider.
To record the analog output voltage, the voltage polarity, and whether the
desired analog output voltage is “running” or “paused,” the user must click the “Record”
button on the front panel. When the record button is on, these parameters as well as the
timestamp are recorded each time the voltage polarity changes. When prompted, the
user should select the file where the parameters were saved previously in order to
append the data to the same file. The user may also save a *.avi movie by clicking the
“Record” button located below the image display. When the user clicks the “stop” button
on the front panel, the program ceases to execute.
Voltage-switching circuit
One of the design goals of the µ-Pong system was to incorporate an easy way to
vary the magnitude of the applied voltage delivered to the microfluidic device. For this
purpose, we utilized a computer-controlled 12-bit digital-to-analog converter, which is a
component of the National Instruments USB-6009 device. However, the output of this
particular device is limited to a unipolar 0-5V range, lacking the ability to reverse the
applied voltage in order to reverse the motion of the flow. Because reversing the
direction of the EOF is the main function of the µ-PONG system, a circuit utilizing
integrated circuit analog switches (74HC4066N) was designed to provide a variable
magnitude and reversible voltage system.
The circuit is powered by a power supply that converts 120V AC voltage to 15V
and -15V (DC voltage). A positive regulator converts the 15V voltage to 5V and a
negative regulator converts the -15V voltage to -5V in order to power five LEDs that
serve as indicators and the integrated circuits (a hex inverter, operational amplifiers, and
a digital switch - see Appendix B for the analog switch datasheet). One LED is
connected to ground such that when it is powered, a voltage is established across it,
indicating that the power is on (see Figure 8). Digital signals two and three are also
connected to current-limited LEDs to indicate whether the system is in manual or
automatic mode and whether the system is paused or running.
The voltage-switching function of the µ-PONG circuitry works by connecting
output amplifiers to either a signal which is equal to the analog input voltage or a signal
which is equal to minus the analog input voltage, depending on whether leftward motion
or rightward motion is required by the control logic signals. Digital signal one serves as
the switch for changing the polarity of the voltage across the microfluidic channel. When
the input signal is at logic 1, “TTL high,” the LED indicating leftward motion is illuminated;
when the signal is at logic 0, “TTL low,” the LED indicating rightward motion is
illuminated, specifying the direction of the voltage across the channel (and the direction
of the EOF). The signal is split between two branches, the first containing one inverter
and the other containing two inverters. Thus, the control signals at the two branches are
7
always at opposite states: when one is at logic “1,” the other is at logic “0.” Because the
particular analog switch integrated circuit utilized in this design requires an input control
signal which defines logic 1 and logic 0 at levels which are not compatible to standard
TTL logic levels, level translating circuitry consisting of diodes and resistors was utilized
to convert TTL level signals to the logic ranges required by the analog switch circuit.
Figure 8: Schematic diagram of the external voltage-switching
circuit. Five LED’s serve as indicators of the power, system modes,
and direction of the EOF. Digital signal one serves as the polarity
switch by routing the analog input voltage signal through one of two
switches that cause the signal to be multiplied by either one or
negative one. The output signals of two operational amplifiers serve
as the voltages sources for the electrodes that establish the electric
field across the channel.
Based on the states of the logic switches, the analog input voltage will either
pass through an operational amplifier, multiplying its value by negative one, or remain
unchanged. (Because digital signal one controls this function, that voltage channel
serves as the voltage polarity switch.) The analog voltage then is amplified by a factor of
1.83 through one operational amplifier and then sequentially multiplied by negative one
through another. Thus, the output electrode connector signals are at +1.83 (Vin) and 1.83 (Vin). Wires from these operational amplifier outputs are connected to gold
electrodes at each end of the channel. Hence, at one electrode, the voltage is +V and at
the other, the voltage is –V. If digital signal one (the polarity switch) changes state, the
input voltages are then multiplied by negative one, changing the direction of the EOF in
the channel.
The voltage switching circuit, DAQ board, and power supply are housed in a
metal box (see Figure 9). The LEDs are visible from the outside of the box, serving as
indicators of whether the power is on, whether the mode is “automatic” or “manual,”
whether the system is “paused” or “running,” and whether the direction of the EOF is
8
“right” or “left.” Two binding post jacks on the outside are the sources of the voltages to
be established at each end of the channel.
Figure 9: Control box containing the USB DAQ device and external
circuit. LED indicators show the status of the system, and two
binding post jacks serve as the sources of the voltage to be
established at each end of the channel.
Three-dimensional particle tracking
Due to pressure differences at each end of the channel, the fluid flow in our
PDMS microchannels may consist of both pressure-driven and electroosmotic flow. We
expect that the speed distribution of particles in the z-dimension of a channel should be
quite different for the two flow types because the driving force for EOF is generated at
the walls of the channel, whereas in the case of pressure-driven flow, the channel walls
serve as friction boundaries that limit the flow velocity. Thus, in order to fully
characterize the fluid flow profile in our PDMS microchannels, the velocity of the beads
in three dimensions must be known. By capturing videos with a camera attached to a
microscope, the velocity of beads in the focal plane may easily be measured. However,
because the beads near the bottom of the channel would require one focus setting, and
beads near the top of the channel would require a completely different focus setting, the
three-dimensional velocity profile of the beads requires a way to characterize the zposition of the bead.
One possible way to characterize the z-dependence of particle velocity would be
to collect data at many different z-values and measure the velocity of in-focus beads at
each altitude. As an alternative technique, a z-axis microscope servo system could be
developed in order to automatically bring a bead into focus, track the bead across the
field of view, and record its z-value over time.
The technique which I have investigated as part of this research involves another
methodology, in which the z-axis position of the bead used for our velocity
measurements is determined by the information encoded in the out-of-focus blur. The zcoordinate of a point source may be found by taking advantage of its point spread
function (PSF), which is defined as the response of an imaging system to a point source.
Because small fluorescent polystyrene beads are quite uniform in size (2.986  0.083
um), they are small enough to behave approximately like point sources at the
magnifications used in these experiments. A point source radiates a complete spherical
wave such that the placement of the lens intercepts a slice of the sphere (see Figure
10). The radius of the image becomes larger as the defocus increases. For even larger
displacements, the image appears as a diffraction pattern of rings, the outermost of
9
which is the brightest ring.9 Thus, the PSF of the bead may be used to identify the
distance of the bead from the focal plane.
Retrieved with permission from:
K. Seale, C. Janetopoulos, and J. Wikswo, ACS Nano 3, 493 (2009).
Figure 10: The 3-dimensional point-spead function (PSF) of a point
source. The collection cone of the microscope objective, shown
here as the “lens,” intercepts a two-dimensional slice of the PSF,
which appears as a pattern of interference rings.
Several strategies for using defocused images to determine the z-coordinate of
the particle position have been developed, including matching the radius vector of a
reference image to that of an experimental image;10 measuring the diameter of the
outermost ring of a defocused particle and using a mathematical formula to determine
the z-coordinate;11 and creating and using a calibration curve based on the radius of the
outermost ring of several reference images.12 The approach used for our data is similar
to the lattermost strategy. Each experimental image was compared to several reference
images with known z-coordinates. The z-component of the velocity may be computed
by determining which reference image matched best and performing a calculation of the
average velocity over several frames.
Initially I used convolution filters to match the reference images to the
experimental image. However, the shape of the intensity distribution prevented an
accurate match, even when normalized several different ways. Better results were
obtained by using a least squares algorithm. For example, if a reference image is
represented by a matrix with entries rij and the experimental image is represented by a
matrix with entries xij , the reference and experimental image match best when S is
minimized:
S    rij  xij  .
2
j 1 i 1
10
To verify that the least squares matching algorithm produced accurate results, S
was computed for several experimental images with known z-coordinates. When the
reference image and experimental image corresponded to the same z-coordinate, the S
value was about an order of magnitude less than the S values for all the other images.
See Table 1 below for an example in which a five-tick image was compared with four
reference images. (The microscope used in these experiments (Zeiss Axiovert 25) has
a z-axis focusing control knob which incorporates uniformly spaced markings, or “ticks,”
which can be used as a quantitative measure of the microscope stage z-axis position.
Each “tick” corresponds to 9.6 microns above the focal plane.) Note that in Table 1,
when the z-coordinates were the same for the experimental and reference image (five
ticks), S was approximately one order of magnitude smaller than any other S value.
Least squares test: 5-tick experimental image
z of reference image
S
1 tick
237856
3 ticks
472564
5 ticks
46473
7ticks
445519
Table 1
I initially made reference images by finding the maximum pixel value (which was
usually located approximately in the center of the off-focus image) and cropping a 71-by71-pixel region of interest (ROI) around that pixel. However, when using this method,
the maximum pixel of the experimental images was often located very far from the
center of the image. To avoid this problem, I instead adopted a centroid-finding method
to determine the center of the image. The calculation shown below, in which I is
intensity, is analogous to finding the center of mass of an object:
 xCM , yCM    


xij I ij
I
ij
,
y I
I
ij ij
ij

 .

Each centered 71-by-71 reference image was then normalized by multiplying each pixel
by 100 and dividing by the maximum value, creating an image with a maximum value of
100. Five or six reference images for each tick were averaged together to create a final
generalized reference image. This was done for z-coordinates of 0-5 ticks at half-tick
intervals (Figure 11).
11
Figure 11: Reference images and their intensity profiles used for
determining the z-value of beads imaged during our experiments.
Each tick corresponds to 4.8 microns in the vertical direction.
The matching algorithm was written as a macro for ImageJ, a Java-based image
processing package (see Appendix C). (All images must be converted to 32-bit TIFF
format prior to running the algorithm in order to avoid pixel saturation.) When the macro
is run, the user is prompted to specify the directory where the image sequence of
experimental data is located. The macro also prompts the user to choose the directory
where the reference images are located. After the first experimental image in the
sequence is opened, the user is prompted to draw a small rectangle around the bead of
interest. The macro then crops the first image down to a 71-by-71-pixel ROI centered on
the centroid of the image. The location of this ROI is saved in a new folder called “roi” in
the same directory. These files may be opened later to ensure that the program has
accurately tracked the particle. Like the reference images, each experimental image is
normalized to have a maximum value of 100. Next, each reference image in the userspecified directory is opened, and S is computed for each reference image. The
filename of the reference image for which S is a minimum is displayed in a “log” window
along with the x- and y-coordinates of the centroid. The algorithm repeats the entire
process for each experimental image in the specified directory, displaying the location of
the bead for each video frame. Using these x-, y-, and z-coordinates and the frame rate
of the video capturing software, an approximation of the particle velocity in threedimensions may then be computed.
Results and Discussion:
Initial experiments confirmed that the µ-PONG system successfully detected the
bead at each goalpost and reversed the EOF upon detection (Figure 12), allowing
experiments to run for extended periods of time. We predicted that the time the bead
12
required to travel from one goalpost to the other (the “transit time”) would remain fairly
constant over short time scales, since the attenuation of EOF should occur over several
hours.8 Since the same volume of fluid should be displaced for every transit, we also
expected that hydrodynamic flow due to differences in fluid height at the ends of the
channel would cancel out in each direction, causing no net fluid displacement. However,
our results indicated that the flow rate varies over periods of tens of seconds (Figure
13a).
Figure 12: A bead controlled by the µ-PONG system moving
between two goalposts.
Transit Time vs. Time
35
Transit Time (s)
30
25
20
15
10
5
0
0
50
100
150
200
250
300
350
400
Time (s)
Figure 13a: The time required for the bead to travel from one
goalpost to another for each transit, plotted versus time.
13
Transit time in each direction vs. time
35
30
Right
Transit Time (s)
Left
25
20
15
10
5
0
0
50
100
150
200
250
300
350
400
Time (s)
Figure 13b: The time required for the bead to travel from one goalpost to
another for each transit, plotted separately for each direction versus time.
After deconstructing the time required for the bead to travel between goalposts in
each direction (Figure 13b), it appeared that the speed of the bead decreased when
traveling to the right but increased over time when moving leftward. The bead then
approached its original speed in both directions after about 350 seconds. Further, the
decrease in speed rightward was about fifteen seconds per transit at its slowest point,
but the increase in speed leftward was always less than five seconds. We surmised that
since the initial transit times to the left and right were not equal, a net hydrodynamic flow
was present, causing the superposition of pressure-driven flow and EOF to complicate
the experiment (Figure 14). Thus, we used a syringe pump to equalize the pressure
before the start of our next trial. In the absence of EOF, the pump introduced more
buffer into the channel until the flow of beads stopped, indicating that the pressure was
equalized. However, the results indicated that although the pressure imbalance was
corrected, the transit times still varied widely throughout the experiment, much like the
first experiment (Figure 15).
PDMS
Hydrodynamic pressure
Electrode
Glass slide
_
Feof
Fh
Bead
+
Goalpost
Figure 14: Superposition of pressure-driven and electroosmotic
flow. If the height of the fluid at one end of the channel is different
from the height at the other end, the imbalance causes pressuredriven flow.
14
Transit Time vs. Time
16
Transit Time (s)
14
12
10
8
6
4
2
0
0
50
100
150
200
Time (s)
Figure 15: The time required for the bead to travel from one
goalpost to another for each transit, plotted versus time. For this
experiment, additional buffer was introduced into one end of the
channel to eliminate the pressure imbalance in the channel.
In all experiments, the bead appeared to move in all three dimensions, instead of
only in the direction parallel to the channel walls. Initially, the ImageJ plugin,
SpotTracker, was used to determine the trajectory of the bead in the channel. However,
this program required the user to click on the bead in each frame in order to compute the
velocity and contained no z-axis information, although the bead drifted out of focus,
indicating motion along the z-axis. Thus, the three-dimensional particle tracking ImageJ
macro was developed to include this information as well as automate the determination
of the x- and y-coordinate of the bead.
A reason that the bead may not only be moving along the x-axis is that, as
mentioned above, a pressure imbalance is present. Because pressure-driven flow has a
parabolic velocity flow profile while EOF has a flat profile (Figure 16), the bead may be
spinning, causing it to move in the direction of the z- and y-axis. The beads also
adhered to the channel walls after a period of about thirty minutes, indicating that
electrostatic or covalent bonds may form between the beads and the wall, perhaps
because the beads accumulate charge. As a test, three-micron carboxylated
polystyrene beads were compared with standard three-micron polystyrene beads. Many
more of the uncoated beads adhered to the channel walls than the carboxylated beads,
which adhered to the walls only after a substantially longer time, if at all. By comparison,
ten-micron polystyrene beads adhered to the walls almost immediately, suggesting that
the weight of the beads may cause sinking and adhesion. These data suggest that an
accurate characterization of the velocity profile in three dimensions is absolutely
essential.
15
Electroosmotic flow
Hydrodynamic flow
Parabolic profile
Flat profile
Figure 16: Hydrodynamic flow has a parabolic profile, while
electroosmotic flow has a flat profile.
In order to test the accuracy of the reference-matching ImageJ macro, we
decided to focus on measuring pressure-driven flow because its properties have been
well studied. Indeed, an analytical solution exists describing the velocity profile of the
fluid within a rectangular channel of a given height (height = 2b) and width (width = 2a).
In the equation of the velocity profile u(y,z),
u ( y, z ) 
 cosh(i z / 2a)  cos(i y / 2a)
16a 2 P 
,
(1)(i 1) / 2 1 


3
 L i 1,3,5,...
i3
 cosh(i b / 2a) 
L is the length of the channel (0.02 meters), µ is the viscosity of water (0.00089 N/m2),
and P is the pressure difference across the channel. The measured velocities were
used to find a numerical value of P in order to calculate the theoretical profile.
Figure 17: The theoretical velocity profile is shown as a green
mesh, while the experimental data points are shown in blue. The
16
blue line is the residual between the velocity profile and
experimental data.
Residual (m/s)
Initially, the experimental data were analyzed by plotting the velocity of the beads
at each z-value (see Appendix D). Parabolas that were fit to these data demonstrate
that the velocity flow profile of the fluid flow in the channel is parabolic except at very low
z-values, due to the effects of friction at the surface of the channel. A plot of y- and zcoordinates versus velocity also demonstrated that higher velocities generally occur near
the middle of the channel, while the flow is relatively slow at the channel edges.
However, in order to fully characterize the velocity profile in three dimensions, the
theoretical velocity curve was calculated and plotted with the experimental data of the
bead velocities analyzed in the channel (see Figure 17). The measured data seemed to
be consistent with the calculated profile expect for low z-values, due to friction near the
edges. The beads at that height probably rolled along the bottom instead of moving with
the flow of the fluid. Beads with z-values greater than about twenty microns were not
observed, perhaps because the density of the beads was lower than that of water,
causing the beads to sink. Differences between the calculated profile and the
experimental data were near or below 0.0001 m/s (see Figure 18). These residuals may
be attributed to approximating the z-value to 4.8 micron intervals. However, these data
suggest that the reference-matching algorithm worked fairly well in determining the
velocity profile in three dimensions and may therefore be used to characterize EOF.
Y (meters)
Figure 18: The difference between the calculated velocity and the
velocity determined experimentally for each y-value.
To demonstrate that beads may be found at all positions in the channel, the
motion of beads flowing under hydrostatic pressure-driven force was recorded and
analyzed in an experiment in which salt water was used as a buffer. Because the
density of polystyrene is 1.05 g/mL, a solution of 10% NaCl in water was made to match
the density of the polystyrene. As shown below (Figure 19), beads were found at all
heights throughout the channel, although most beads were found near the center. This
was due to the fact that the beads move faster in the center of the channel, thereby
allowing more beads to be observed there during a given time. Hence, experiments may
17
be done with a buffer of about the same density as polystyrene so that the velocity
profile may be calculated based on beads at all z-values in the channel.
Bead Height Distribution
40
Number of Beads
35
30
25
20
15
10
5
0
0
4.8
9.6
14.4
19.2
24
28.8
33.6
38.4
43.2
48
Z (microns)
Figure 19: The number of beads observed at each z-value.
Conclusions and Future Directions:
The results of our experiments have shown that the µ-PONG system precisely
controls the movement of polystyrene beads by manipulating the electroosmotic flow
within a PDMS microchannel. The analysis software, an ImageJ macro, has proven to
be approximately accurate in determining the three-dimensional velocity profile of
pressure-driven flow in the channel. Thus, the system and analysis methods should
prove useful for characterizing EOF in the channel over time.
In the future, this system should be used to study the three-dimensional velocity
profile of EOF in the channel to characterize its attenuation over time. We expect that
the analysis of such experiments would demonstrate that pressure-driven flow and EOF
occur simultaneously. Further studies would also determine the reason that the motion
of the beads fluctuates as observed, implicating the properties of the flow. Once the
EOF is characterized for a single channel, the system may then be used to study the
fluid dynamics through more complicated microfluidic devices. This information may
then be used for designing and optimizing those devices as well as predicting the
movement of fluid within the channels.
This system may also be used to deliver fluid in a tightly controlled manner in a
microfluidic channel. Such applications may include LOC devices that require careful
control of a fluid pump. Other applications include the manipulation of micro- or
nanoscale objects, such as particles or cells. Hence, µ-PONG should serve as a
method for discovering the properties of fluid flow in microdevices and may potentially
serve as a part of other microfluidic systems for studying biology.
18
References:
1
2
3
4
5
6
7
8
9
10
11
12
S. K. Sia and G. M. Whitesides, Electrophoresis 24, 3563 (2003).
L. Cui, D. Holmes, and H. Morgan, Electrophoresis 22, 3893 (2001).
A. E. Cohen and W. E. Moerner, Physical Review Letters 98, 116001 (2007).
D. A. Skoog, F. J. Holler, and S. R. Crouch, Principles of Instrumental Analysis
(Thomson Brooks/Cole, Belmont, CA, 2007).
W. Hellmich, J. Regtmeier, T. T. Duong, R. Ros, D. Anselmetti, and A. Rox,
Langmuir 21, 7551 (2005).
G.-B. Lee, C.-H. Lin, K.-H. Lee, and Y.-F. Lin, Electrophoresis 26, 4616 (2005).
X. Y. Wang, C. Cheng, S. L. Wang, and S. R. Liu, Microfluidics and Nanofluidics 6,
145 (2009).
X. Ren, M. Bachman, C. Sims, and G. P. Li, Journal of Chromatography B 762, 117
(2001).
M. Mansuripur, Journal of the Optical Society of America A - Optics Image Science
and Vision 3, 2086 (1986).
Z. Zhang and C. Menq, Applied Optics 47, 2361 (2008).
M. Speidel, A. Jonas, and E. Florin, Optics Letters 28, 69 (2003).
S. Peterson, H. Chuang, and S. Wereley, Measurement Science & Technology 19
(2008).
19
Acknowledgements:
I would like to gratefully acknowledge Phil Samson, Dmitry Markov, and John Wikswo for
their mentorship and assistance throughout this project. I would also like to thank Dawit
Jowhar for his help in creating the LabView program by designing the imaging and
detection components of the system. Finally, I would like to acknowledge the Vanderbilt
Institute for Integrative Biosystems Research and Education, the William A. and Nancy
F. McMinn Foundation, and the Systems Biology and Bioengineering Undergraduate
Research Experience for the opportunity and funding to do this research.
20
Appendix A:
LabView Block Diagram
NO
YES
Switch polarity?
AND
Start session
MANUAL
Manual/auto mode?
AUTO
Create buffer
NO
Run?
Find connected cameras?
NO
YES
User Inputs
Control camera
settings
YES
Set min/max voltage
Send zero
volts to
channel
Acquire image
Display image
YES
Send analog
voltage to
channel
Paused?
NO
Set digital channel
Acquire intensity of
goalpost pixels
Is pixel above
threshold?
NO
(Left goalpost)
Set pixel threshold
YES
Was threshold
previously
reached at right
goalpost?
Set analog channel voltage
Save data?
NO
NO
YES
21
YES
Change state of
digital
channel one
Did state of
channel change
from previous
state?
NO
YES
Write data
to file
Is pixel above
threshold?
(Right goalpost)
AND
NO
YES
Was threshold
previously
reached at left
goalpost?
NO
YES
Appendix B: Analog Switch Datasheet
22
23
24
Appendix C: 3-D Tracking ImageJ Macro
dirSeq = getDirectory("Choose the directory where the image sequence is located");
files = getFileList(dirSeq);
File.makeDirectory(dirSeq+"\\roi")
dir = getDirectory("Choose the directory where the reference images are located");
list = getFileList(dir);
for (i=0; i<files.length; i++) {
open(dirSeq + files[i]);
currentFile = File.getName(dirSeq + files[i]);
if(i==0){
getSelectionBounds(p,q,w,h);
if(p==0){
waitForUser("Draw a small rectangle around the bead, then click
OK");
getSelectionBounds(p,q,w,h);
xcenter = round(p + w/2 - 35);
ycenter = round(q + h/2 - 35);
}
}
run("Specify ROI", "roi width=70 height=70 x="+xcenter +" y="+ycenter+" slice=1");
run("Crop");
showStatus("Finding centroid...");
width = getWidth();
height = getHeight();
yadd = 0;
xadd = 0;
total = 0;
for (y=0; y<height; y++) {
if (y%20==0) showProgress(y, height);
for (x=0; x<width; x++) {
intensity = getPixel(x,y);
xnum = intensity*x;
ynum = intensity*y;
yadd = yadd + ynum;
xadd = xadd + xnum;
total = total + intensity;
}
}
xcentroid = xadd/total;
ycentroid = yadd/total;
xcorner = round(xcentroid - 25);
ycorner = round(ycentroid - 25);
showStatus("Cropping region of interest...");
run("Specify ROI", "roi width=51 height=51 x="+xcorner+" y="+ycorner+" slice=1");
saveAs("Selection", dirSeq+"\\roi\\"+currentFile+".roi");
run("Crop");
25
showStatus("Normalizing...");
showStatus("Finding pixel with largest value...");
width = getWidth(); height = getHeight();
max=0;
for (y=0; y<height; y++) {
if (y%20==0) showProgress(y, height);
for (x=0; x<width; x++) {
value = getPixel(x,y);
if (value>max) {
max = value;
xmax = x;
ymax = y;
}
}
}
run("Divide...", "value="+max);
run("Multiply...", "value=100");
large = 1000000000;
tick = "unknown";
for (j=0; j<list.length; j++) {
open(dir + list[j]);
ref = File.getName(dir + list[j]);
imageCalculator("Difference create 32-bit", currentFile, ref);
//run("Image Calculator...", "image1="+currentFile+" operation=Difference
image2="+ref+" create 32-bit");
run("Square");
showStatus("Summing pixel values...");
width = getWidth();
height = getHeight();
for (y=0; y<height; y++) {
if (y%20==0) showProgress(y, height);
for (x=0; x<width; x++) {
value = getPixel(x,y);
sum = sum + value;
}
}
close();
close();
if (sum<large){
tick = ref;
large = sum;
}
sum = 0;
}
print(tick+","+round(xcentroid+xcenter)+","+round(ycentroid+ycenter));
close();
xcenter = xcorner + xcenter - 15;
ycenter = ycorner + ycenter - 5;
}
26
Appendix D: Preliminary Data Analysis of Pressure-Drive Flow
Velocity vs. Y for Z = 0 microns
Velocity vs. Y for Z = 14.4 microns
100
250
90
200
70
Velocity (um/s)
Velocity (um/s)
80
60
50
40
30
150
100
50
20
0
10
0
R2 = 0.3612
10
20
30
40
0
10
20
30
40
50
60
R2 = 0.9972
0
50
-50
60
Y (microns)
Y (microns)
Velocity vs. Y for Z = 19.2 microns
Velocity vs. Y for Z = 9.6 microns
250
250
200
Velocity (um/s)
150
100
150
100
50
50
0
0
R2 = 0.9864
10
20
30
-50
0
10
20
30
40
50
60
Y (microns)
Y (microns)
Velocity vs. Position
60
50
40
30
20
10
0
0
10
40
50
R2 = 0.9594
0
Z (microns)
Velocity (um/s)
200
30
20
40
50
60
-10
Y (microns)
(The area of each circle corresponds to the velocity of the bead at that position.)
27
60
28